Estimation and Vanishing Results for Hodge numbers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866912055889494016 |
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| author | Petersen, Peter Wink, Matthias |
| author_facet | Petersen, Peter Wink, Matthias |
| contents | We show that compact Kähler manifolds have the rational cohomology ring of complex projective space provided a weighted sum of the lowest three eigenvalues of the Kähler curvature operator is positive. This follows from a more general vanishing and estimation theorem for the individual Hodge numbers. We also prove an analogue of Tachibana's theorem for Kähler manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_14319 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Estimation and Vanishing Results for Hodge numbers Petersen, Peter Wink, Matthias Differential Geometry Complex Variables 32Q10, 32Q15, 32Q20, 53C21, 53C55 We show that compact Kähler manifolds have the rational cohomology ring of complex projective space provided a weighted sum of the lowest three eigenvalues of the Kähler curvature operator is positive. This follows from a more general vanishing and estimation theorem for the individual Hodge numbers. We also prove an analogue of Tachibana's theorem for Kähler manifolds. |
| title | Estimation and Vanishing Results for Hodge numbers |
| topic | Differential Geometry Complex Variables 32Q10, 32Q15, 32Q20, 53C21, 53C55 |
| url | https://arxiv.org/abs/2009.14319 |